Shangri La is the historic home of Doris Duke in Honolulu.
It is filled with installations of Islamic tilework and other arts. Open
to the public in late 2002, by reservation for tours arranged through the
Honolulu Academy of Arts, today this home serves as a museum in which a
walking tour can provide extraordinary visual opportunities for the study
of geometry and pattern both in the arts that are installed and exhibited,
and in the surrounding plantings and landscape. The house offers a plethora
of educational opportunities, for which its full potential has not yet
been tapped. A new initiative in 2004 afforded us the possibility of collaboration
during a two-week scholarly residency, which we wish to share in this paper
and presentation. What we offer here is a sampling of what we encountered
through photographic documentation, analysis, and discussion.

Hidden and secluded on the lava rocks of Black Point (fig.
2), projecting into the Pacific beyond Diamond Head in Honolulu, is
Shangri La, built as a home and quiet retreat for Doris Duke, one of the
richest American women of all time. After she died in 1993, her will stipulated
that Shangri La would be operated by the Doris Duke Foundation for Islamic
Art, and opened to the public for the "promotion and study of Middle Eastern
arts and cultures" [10]. Her last will and testament
disclosed this private domain for public enjoyment, revealing that it served
as a repository for sixty years of her passionate collecting and personal
display of Islamic art, set amidst tropical foliage of palms, Norfolk pine,
ferns, croton, and bougainvillea. Typical of Islamic art generally, the
works exhibit a wide variety of geometric patterns based on symmetrical
relationships among the designs [1, 4,
5,
6, 14, 15,
16].
But unlike many European and American museum collections, which were acquired
with an eye for Western paradigms of art appreciation, the collections
at Shangri La are unique in the United States in many ways: Their permanent
display is in the context of a private home built in the style of American
modernism; the sheer quantity of materials from Islamic lands is enormous
(approximately 3500 objects), and these contribute to an ambience that
is quintessentially personal yet filled with visual, literary, and cultural
allusions; the display of works of Islamic art in a tropical environment
contributes to a sensuality with which one may appreciate the symmetries,
antisymmetries, and underlying geometric structure of forms in art and
nature in one breath. Most of the individual built components of the home
bear axes of strict symmetry (fig. 3).

Figure 2: Shangri La, viewed from the west Figure 3: Symmetry in the orientation of built components

2. Islamic Art: Symmetry and Pattern

Patterns in Islamic art are usually organized according
to principles of symmetry [1,2], articulating geometric relationships among
forms [4,6,15].
Such patterns represent algorithmic iterations of individual design units
[5,14] and may allude to metaphysical
concerns [3,6]. At Shangri La, what
is installed includes painted wood panels (fig. 4), molded
and glazed ceramic tiles (figs. 1; 14-15),
inlaid wood and metalwork, embroidered, appliquéd, and woven textiles
(fig. 4), blown and molded glass (fig.
4), and cut stone pavements and panels (figs. 5-9),
gathered from regions of the Islamic world as diverse as Spain, Morocco,
Egypt, Syria, Turkey, Iran, and India. Doris Duke also commissioned works
in Islamic styles for installation in her home from India, Morocco, Iran,
and Hawaii.

Many of the patterns show symmetry in their composition,
no matter what the material. Reflections, and reflections of reflections,
are present throughout the house. In the works of Islamic art, vertical
and/or horizontal reflection is often present, as is rotational symmetry,
with orders 2, 3, 4, 6, and 8 most prevalent. Looking at individual centers
of rotation, around which local sections of patterns rotate (disregarding
color), we can see among the plane symmetry groups families of patterns
with 2-4-4 rotocenters (figs. 1, 7)
and 2-3-6 rotocenters (figs. 8-9) [12,
13]:

Patterns with related relationships of forms and rotational
symmetries appear and reappear throughout the house. Among the carved marble
screens (called jali), imported from India and used in the bedroom
and in the pavilion above the bedroom (fig. 10), there
is also an example of a pattern with 2-3-6 rotocenters (fig.
11), showing hexagons and six-pointed stars set within a larger pattern
of interlaced hexagons.

Figure 10 (left): Pavilion above Bedroom with
carved marble screens

Figure 11 (right): Detail, carved marble screen
with 2-3-6 pattern

This pattern served as the basis for commissions of carved
wooden doors, probably made in Hawaii (fig. 12). Patterns
using hexagons, with or without six-pointed stars, is a decorative scheme
used throughout the house. Other commissioned doors and gates reflect the
direct influence of other works of Islamic art Miss Duke had acquired.
A small gate (fig. 13) leading to roof access above
the Playhouse utilizes a pattern related to that of the tilework
in the courtyard (figs. 1, 14-15)
with 2-4-4 rotocenters. These tilework panels show the illusion of interlace
(fig. 1), effected by molded tiles. Each panel (figs.
14-15) is composed of two sets of tiles; both sets are molded and selectively
glazed. One set shows an eight-pointed star shape with a molded central
hemispherical boss decorated with floral elements with approximate order
4 rotational symmetry, off axis with the surrounding eight-pointed star.
The other set comprises square tiles, with a corner cut to match the outline
of a quarter eight-pointed star. This tile is also molded, and bears four
crossed bands, which when repeated four times creates an illusionary interlaced
form with eight extensions. The negative spaces created by the generation
of this pattern are irregular five-pointed stars, and octagons. The tiles
of the two side panels (fig. 14) are minimally glazed;
only the eight-pointed star tile and one corner of each square tile is
glazed. In contrast, the tiles of the central panel (fig.
15) show glazing of both the eight-pointed star tiles with molded boss,
and in all of the polygonal areas surrounded by interlace. Each of the
polygons also contains molded floral elements the raised surfaces of which
cause pooling of the glaze, which creates additional visual effects.

For both panels, the glazes are a cobalt blue and a copper-based
turquoise. Parallels for these tile panels have been excavated at the site
of Takht-i Suleiman in western Iran, dating from the early 13th
century [9].

This pattern, with an underlying square grid and several
different forms of concentric eight-pointed stars, was also taken as the
basis for several commissions at Shangri La. The underlying square grid
is emphasized in the Playhouse gate (fig. 13). The pattern
also served for the design of painted and resin-coated panels for the ornamented
ceiling of the Playhouse lanai.

4. Border Patterns

Border patterns with floral design elements show a variety
of line symmetries (fig. 16a-c), often taking advantage
of the inherent ambiguities seen in the use of reflections and glide reflections,
in which there is also a rotational symmetry present (fig.
16a) [2], combined with symmetry-breaking.

Figure 16 (a,b): Ceramic tile;(c): Ceramic mosaic

5. Dilation and Projection

In the central courtyard, a patio called by Doris Duke
"Pure Persian" [7, p. 75], is a set of twelve columns
which exhibit dilation and projection (fig. 17). These
were manufactured in Chicago according to Miss Duke’s specifications, and
later set with mirrored surfaces in Hawaii. The design is based upon the
tall narrow columns with muqarnas capitals, typical of courtly monuments
in Safavid Isfahan dating from the 17th century. Set on a square
base, the shaft of each column is a tapering octagonal prism. At the top
of the column shaft (fig. 18), the capital, in contrast,
exhibits a transition from the octagonal cross-section of the column, progressing
in a stacked series of eight-pointed star prisms alternating with antiprism-like
solids in which each triangular element is folded in the center. At the
top of each capital is a square prism.

Doris Duke (fig. 22) can be seen to
have amused herself by playing amply with form and structure, not only
in the grouping of works of art, which she tended to rearrange at every
visit [10], but also in the placement and orientation
of individual works. She played with axes of symmetry, emphasizing vistas
and focusing attention on particular objects [7]. She
also made visual reference among objects and plantings. For example, the
twined Indian laburnum tree planted beside the fountain (fig.
1) breaks the symmetry of the courtyard, but it also replicates the
intertwined tree represented in nearby Safavid tile panels (fig.
17), the Persian reference a metaphor of lover and beloved. Miss Duke
also took liberties in the placement of works to suit her particular sense
of aesthetics. A tile panel meant to be viewed horizontally (fig.
19), she mounted vertically to suit the view down a corridor (fig.
20).

The plantings and landscaping (fig. 21)
reinforce the use of natural forms within the built environment. Among
the lush vegetation selected by Miss Duke for use at Shangri La, there
are many specimens the form and structure of which contribute to an appreciation
of the relationships between the patterns of nature and the nature of patterns.
This is a site that warrants careful, slow, studied observation to reveal
a broadened understanding of patterns [8] that enrich
the diversity of our world.